Ramp: Forces and motion

Use an on-line simulation from the University of Colorado PhET group to explore the behavior of objects that are just placed on, or pushed up and down a ramp.

A free body diagram of an object on a frictionless ramp is shown above.   The y-component of the weight mg of the object is exactly canceled by the normal force of magnitude N.  The x-component of the weight accelerates the object down the ramp.

On a real ramp the object and the ramp will interact via the frictional force.  The coefficients of static friction, μ_s, and kinetic friction, μ_k, which depend on the type of surfaces that are in contact with each other, are used to calculate the maximum force of static friction and the force of kinetic friction.

f_s ≤ μ_sN,  f_k = μ_kN.

The frictional force always points in a direction to oppose the relative motion of the surfaces.
For the interaction between the object and the ramp f_{s_max} = μ_smg cosθ,  f_k = μ_kmg cosθ.

Procedure:

Open the" Ramp:  Forces and Motion" simulation.
Link to the simulation:  https://phet.colorado.edu/en/simulations/legacy/ramp-forces-and-motion

Explore the interface!

• Try the different tabs at the top of the simulation.  Concentrate on the first three tabs.
• Explore the options in the panel on the right side of the simulation.

Answer the following questions.

(a)  Place the small crate on the ramp with a ramp angle of 20^o.  Click play.  Slowly increase the ramp angle.  What is the smallest angle at which the block starts to move?
Use this angle to calculate μ_s and compare to the given value for μ_s for the crate.
(b)  Place the crate on the the 30^o ramp at the 8 m position.  Click play.  What is the magnitude of the acceleration of the crate, as it accelerates down the ramp?   
(c)  Place the crate on the the 30^o ramp at the 8 m position.  Click play.  At what position does it come to rest?
(d)  What is the coefficients of static friction μ_s for the Mystery Object?
(e)  What is the coefficients of kinetic friction μ_k for the Mystery Object?

Now go to Canvas, Assignments, Extra Credit 5.  Answer questions 1 - 5.  You can submit twice and the highest score counts.